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Pontryagin Duality and the Structure of Locally Compact Abelian Groups Sidney A. Morris

Pontryagin Duality and the Structure of Locally Compact Abelian Groups By Sidney A. Morris

Pontryagin Duality and the Structure of Locally Compact Abelian Groups by Sidney A. Morris

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Summary

These lecture notes begin with an introduction to topological groups and proceed to a proof of the important Pontryagin-van Kampen duality theorem and a detailed exposition of the structure of locally compact abelian groups. Measure theory and Banach algebra are entirely avoided and only a small amount of group theory and topology is required.

Pontryagin Duality and the Structure of Locally Compact Abelian Groups Summary

Pontryagin Duality and the Structure of Locally Compact Abelian Groups by Sidney A. Morris

These lecture notes begin with an introduction to topological groups and proceed to a proof of the important Pontryagin-van Kampen duality theorem and a detailed exposition of the structure of locally compact abelian groups. Measure theory and Banach algebra are entirely avoided and only a small amount of group theory and topology is required, dealing with the subject in an elementary fashion. With about a hundred exercises for the student, it is a suitable text for first-year graduate courses.

Table of Contents

1. Introduction to topological groups; 2. Subgroups and quotient groups of Rn; 3. Uniform spaces and dual groups; 4. Introduction to the Pontryagin-van Kampen duality theorem; 5. Duality for compact and discrete groups; 6. The duality theorem and the principal structure theorem; 7. Consequences of the duality theorem; 8. Locally Euclidean and NSS-groups; 9. Non-abelian groups.

Additional information

NLS9780521215435
9780521215435
0521215439
Pontryagin Duality and the Structure of Locally Compact Abelian Groups by Sidney A. Morris
Sidney A. Morris
London Mathematical Society Lecture Note Series
New
Paperback
Cambridge University Press
1977-08-04
140
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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